Problem: Find $\dfrac{d}{dx}(7\cdot10^x)$. Choose 1 answer: Choose 1 answer: (Choice A) A $7\log(x)\cdot 10^x$ (Choice B) B $7\cdot 10^x$ (Choice C) C $7\cdot 10^{x-1}$ (Choice D) D $7\ln(10)\cdot 10^x$
Solution: The expression to differentiate includes an exponential term. Remember that the derivative of the general exponential term $a^x$ (where $a$ is any positive constant) is $\ln(a)\cdot a^x$. Put another way, $\dfrac{d}{dx}(a^x)=\ln(a)\cdot a^x$. $\begin{aligned} &\phantom{=}\dfrac{d}{dx}(7\cdot10^x) \\\\ &=7\dfrac{d}{dx}(10^x) \\\\ &=7\cdot\ln(10)\cdot10^x \end{aligned}$ In conclusion, $\dfrac{d}{dx}(7\cdot10^x)=7\ln(10)\cdot 10^x$.